Cut the onion and bell pepper into thin strips. Thin pieces cook quickly and fit neatly on a bun. Big chunks are hard to bite through and can slide out of the sandwich.
Put the sliced vegetables in a bowl and drizzle in the olive oil. Add a dash of salt and pepper, then toss until everything is coated. This light coating helps the vegetables soften and pick up flavor in the pan.
Set your cast iron skillet over medium-high heat on the stove and let it warm up for a few minutes. A properly hot pan gives the brats that golden crust. If you cook outdoors, place the skillet on the grill instead.
Lay the brats in the hot skillet and turn them until every side has color. This takes about 5 minutes. You are not cooking them through yet, just building flavor on the outside.
Scatter the peppers and onions around the brats. Pour in the beer slowly, since a hot pan makes it foam. If the skillet is small, add half first, wait for it to settle, then add the rest.
Put the lid on, or cover tightly with foil, and lower the heat to medium. Let everything simmer for 15 to 20 minutes. The vegetables should be soft and the beer mostly reduced to a light glaze.
Take the skillet off the heat and let the brats rest for a couple of minutes. Tuck each brat into a bun and pile on the peppers and onions. Add mustard or sauerkraut if you like, and serve right away.